Acoustic signal-based position tracking systems may be used with mobile devices such as smartphones, tablets, and laptops. Moreover, acoustic signal-based position tracking systems may be used with basically any computing device that has a screen. One example of an acoustic signal-based position tracking system is a digital pen having an acoustic signal transmitter that is in communication with a receiver that is a computing device, where the digital pen is used to interact with the computing device.
A conventional acoustic signal-based position tracking system includes a transmitter that emits acoustic signals and a receiver that receives the emitted signals. The receiver measures the propagation delay, referred to as Time of Arrival (“TOA”), of the received acoustic signal, and may multiply the TOA by the speed of sound, to determine a position of the transmitter. Using multiple receivers may allow triangulation and/or another form of multilateration, and provide for the determination of a position in two or even three dimensions. A tracking system that uses TOA to determine a position may have performance limitations and have suboptimal accuracies when the transmitting device is not in contact with the computing device. Further, additional timing synchronization or sound speed estimation functions may be needed to mitigate the localization errors.